||Active transport of cargoes is critical for cellular function. To accomplish this, networks of cytoskeletal filaments form highways along which small teams of mechanochemical enzymes (molecular motors) take steps to pull associated cargoes. The robustness of this transport system is juxtaposed by the stochasticity that exists at several spatial and temporal scales. For instance, individual motors stochastically step, bind, and unbind while the cargo undergoes nonnegligible thermal fluctuations. Experimental advances have produced rich quantitative measurements of each of these stochastic elements, but the interaction between them remains elusive. In this thesis, we explore the roles of stochasticity in motor-mediated transport with four specific projects at different scales. We first construct a mean-field model of a cargo transported by two teams of opposing motors. This system is known to display bidirectionality: switching between phases of transport in opposite directions. We hypothesize that thermal fluctuations of the cargo drive the switching. From our model, we predict how cargo size influences the switching time, an experimentally measurable quantity to verify the hypothesis. In the second work, we investigate the force dependence of motor stepping, formulated as a state-dependent jump-diffusion model. We prove general results regarding the computation of the statistics of this process. From this framework, we find that thermal fluctuations may provide a nonmonotonic influence on the stepping rate of motors. The remaining projects investigate the behavior of nonprocessive motors, which take few steps before detaching. In collaboration with experimentalists, we study seemingly diffusive data of motor-mediated transport. Using a jump-diffusion model, the active and passive portions of the diffusivity are disentangled, and curious higher order statistics are explained as a sampling issue. Lastly, we construct a model of cooperative transport by nonprocessive motors, which we study using reward-renewal theory. The theory provides predictions about measured quantities such as run length, which suggest that geometric effects have a large influence on the transport ability of these motors.